Strong and weak constraints in disjunctive datalog

This paper presents an extension of disjunctive datalog (Data-log∨,⌝) by integrity constraints. In particular, besides classical integrity constraints (called strong constraints in this paper), the notion of weak constraints is introduced in the language. These are constraints that are satisfied if possible. The semantics of weak constraints tends to minimize the number of violated instances. As a consequence, weak constraints differ from strong constraints only if the latter are unsatisfiable. Weak constraints may be ordered according to their importance to express different priority levels. The formal definition of the semantics of weak constraints is given in a general way that allows to put them on top of any existing (model-theoretic) semantics for Datalog∨,⌝ programs. A number of examples shows that the proposed language (call it Data-log∨,⌝, c) is well-suited to represent complex knowledge-based problems, such as, for instance, NP optimization problems.A detailed complexity analysis of the language is given as well as an algorithm for the computation of the stable model semantics of Datalog∨,⌝c programs.